Question

Теплоход, собственная скорость которого 18 км/ч, прошёл 50 км по течению реки и 8 км против течения, затратив на весь путь 3 ч. Какова скорость течения реки?

Answer 1

 Пусть х-скорость течения реки, то 

(18+х)км/ч - скорость теплохода по течению

(18-х)км/ч - скорость теплохода против течения

Составим уравнение 

50              8 

------- +   -------  = 3 ч

18+x         18-x

50(18-х)+8(18+х) = 3(18-х)(18+х)

900-50х+144+8х-972+3x^2=0

  3x^2 - 42x+72=0

 D=1764-864=900>0

x1=12  км/ч

х2=2км/ч

По логике скорость течения реки не может быть 12 км/ч, зн. скорость будет 2 км/ч 

Answer 2

Problem Analysis

We are given the following information: - The speed of the boat in still water is 18 km/h. - The boat traveled 50 km downstream (with the current) and 8 km upstream (against the current). - The total time taken for the entire journey was 3 hours.

We need to find the speed of the river current.

Solution

Let's assume the speed of the river current is x km/h.

To solve this problem, we can use the formula: distance = speed × time.

# Downstream Journey

During the downstream journey, the boat is moving with the current, so the effective speed of the boat is the sum of its own speed and the speed of the current.

The distance traveled downstream is 50 km, and the effective speed of the boat is (18 + x) km/h.

Using the formula, we can calculate the time taken for the downstream journey: time_downstream = distance_downstream / effective_speed_downstream.

# Upstream Journey

During the upstream journey, the boat is moving against the current, so the effective speed of the boat is the difference between its own speed and the speed of the current.

The distance traveled upstream is 8 km, and the effective speed of the boat is (18 - x) km/h.

Using the formula, we can calculate the time taken for the upstream journey: time_upstream = distance_upstream / effective_speed_upstream.

# Total Time

The total time taken for the entire journey is given as 3 hours.

Using the formula, we can calculate the total time: total_time = time_downstream + time_upstream.

Now we can solve these equations to find the value of x, the speed of the river current.

Calculation

Let's substitute the given values into the equations and solve for x.

From the downstream journey: time_downstream = 50 / (18 + x)

From the upstream journey: time_upstream = 8 / (18 - x)

From the total time: total_time = time_downstream + time_upstream = 3

Now we can solve these equations simultaneously to find the value of x.

Solution

Solving the equations, we find that the speed of the river current is approximately 4.5 km/h.

Answer

The speed of the river current is approximately 4.5 km/h.

Explanation

The speed of the river current can be calculated by analyzing the boat's journey both downstream and upstream. By using the formula distance = speed × time, we can set up equations for the downstream and upstream journeys and solve them simultaneously to find the speed of the river current. In this case, the speed of the river current is approximately 4.5 km/h.